Time series are data observed over time (either in continuous time or at discrete time periods).

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75 views

help on how to include term $\exp(β_t)/(1+\exp(β_t))$ in AR(2) model

I am trying to include a term in an AR(2) model: $$Y_t=\left( a_0+a_1 \frac{\exp(\beta_t)}{1+\exp(\beta_t)}\right)Y_{t-1}+bY_{t-2}+\delta\epsilon_t$$ Can anyone please help me with this? I don't seem ...
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117 views

Determining the best correlated time series

Before asking, I read similar questions, but none of them lead to satisfying answers for my specific interest. I want to homogenize a climate time series of precipitation of the Dominican Republic ...
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20 views

Predicting a Certain Type of failure and deciding the input time series

I am trying to predict the time to certain type of failure given the following data on Certain Factory Equipments. The data I have are readings collected every day for sensor installed on those ...
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26 views

What is usefulness of time series decomposition if building a multivariate model?

I am at the early stages of building a panel regression model of sales data. I know my final model dataset will consist of log sales, control variables and log media variables. I am planning to use ...
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2answers
124 views

Standard error of regression coefficients without an assumption of homoscedastic normal noise

I have a time series that is affected by two (or more) kinds of events. When event $A$ happens, some signal is linearly added to the time series (the signal lasts, for example, for 100 time points). ...
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10 views

Calculating a smooth 90% limit for differences in a time series

I have 50 data sets. Each set has three related time series: fast, medium, slow. My end purpose is simple, I want to generate a number that indicates a relative degree of change of the time series at ...
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34 views

Data mining of time series

I have a dataset which consist of n time series variables $X_1$..$X_n$ , and a time serie output $Y$. I would like to mine the data to find if some functions (lagged or not) of the $X_i$ can predict ...
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80 views

Probability puzzle about zombies

I am thinking about writing a simple game about zombies. I got stuck trying to calculate how many people should become zombies. Here are my conditions: We have a small rural town of 700 people. One ...
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41 views

How do I statistically compare two time series of different length?

If I have two completely different time series at equally sampled times, but the length of each of these series is different. How do I statistically compare them? Dynamic Time Warping? Also, as a ...
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63 views

Performance testing: detecting changes in distributions over time

I have an interesting application I’d like some advice on. A common task when working with stochastic systems in an engineering context is testing for regressions and improvements in performance. ...
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45 views

ar() time series function in R, manually checking the residuals/predicted values

I am using the ar() function to fit an AR model to some data, and this object will return the in sample residuals. I also know the syntax for how to get the corresponding predicted values, but I want ...
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42 views

Modeling techniques for dichotomous data

I have dichotomous data where some of my independent variables are categorical, some are continuous and some are binary (0/1). My dependent is a binary response (Fail/NoFail, 0/1). The data is some ...
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30 views

Longitudinal panel dataset: Consequences of missing values

I am analyzing a longitudinal panel dataset using OLS. The data spans around 40 years, but for some variables data was unavailable for certain categories. In most cases, the data for given category ...
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27 views

What is the correct specification for a segmented regression of interrupted time series data with a non-equivalent comparison group?

I know this is the general specification for a single group: $Y_i$ = $\beta_0$ + $\beta_1$*time + $\beta_2$*post + $\beta_3$*timepost where time is a continuous ...
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32 views

fpp forecasting using AWS ubuntu

Is the package fpp (or any of its previous incarnations like forecast) supported in Ubuntu 12.04 using AWS? It is the only package that R downloads but when you load the library it throws an error. ...
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42 views

NIST exponential smoothing formula

I am trying to relate data and results in NIST website with the formula defined in previous page from the same website. But I am missing something here: Does initial trend & season indices ...
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42 views

Calculating standard deviation after spatially and temporally averaging data

I have a spatio-temporal data set with (n,m) spatial and k temporal dimensions. My initial analysis consisted of spatially averaging the data and looking at the time dependent behavior. This resulted ...
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38 views

What are the potential problems associated with using negative binomial regression with random effects?

Are there any major potential problems with using negative binomial regression (xtnbreg) with random effects and lagged dependent/independent variables. (Time-series cross-section data) I'm analyzing ...
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190 views

R detect increasing/decreasing trend of time series

I have lots of time series with periods: day, week or month. With stl() function or with loess(x ~ y) I can see how trends of ...
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11 views

SARIMA (1,1,0)x(1,0,0) [duplicate]

Can anyone please write out the model of the ARIMA(1,1,0)x(1,0,0) with AR(1) coef 0.0902 SAR(12) coef 0.107 constant 0.15. Am really confused with how the model should look like
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65 views

How to use one time series to predict another?

Note: There is another post with very similar title, but it is really on the author's specific problem with submarines. Mine is more general. I have asked a similar question before but turns out it ...
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1answer
94 views

Cross-correlation in Matlab

What is the difference between: 1) xcov(x,y,10,'unbiased')/sqrt(xcov(x,x,0,'unbiased')*xcov(y,y,0,'unbiased')); 2) xcorr(x,y,10,'unbiased'); 3) [A, B] = crosscorr(x,y,10); ? I think (but I am not ...
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93 views

Holt-Winters exponential smoothing formula

I am trying to implement Holt-Winters exponential smoothing in Java program (I understand that R and Python have implementations of these algorithms, but I can't use those due to other reasons, so ...
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31 views

Clustering time-shifted sales time-series

I need to perform clustering and classification of time series of weekly sales of different products. My data are weekly sales of different products in differest areas (stores). The challenges on this ...
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41 views

Time series degree of slope: calculating what I see

I want to calculate the degree of slope at each point in a time series. Different time series have different scales. The final number should be normalized in the range of +/-90 degrees. Basically, ...
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69 views

How to get the true mean forecast using the Arima package with a Box-Cox transformation

In the Arima package, using a Box-Cox transformation give wrong results when later applied to the forecast method. For example, consider this data: ...
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17 views

R - Network Connectivity over the time

I have to analyze if a network (represented as a graph) mantains its connectivity over the time. The data that I've obtained from the simulation is given here, where L1 points out the vertex of the ...
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28 views

Derivation of Zhou (1996) volatility estimator

Does anyone know how to derive the Variance of Bin Zhou's volatility estimator (Theorem 1) in 'High-Frequency Data and Volatility in Foreign-Exchange Rates' (1996)? PDF Link attached. Any help would ...
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37 views

What to do if transformed data still has unstable variance

After using Bartlett test statistics for equal variance to test my data, i concluded that there was significant difference in the variance at alpha = 0.05. I transformed the data using Box-Cox family ...
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139 views

How to interpret ACF and PACF and compare with Ljung Box result

I took the residual of a historical stock price $\hat e_t=r_t-\hat \mu_t$, where $r_t$ is the return of a stock and ran ACF and PACF. From the ACF I think that the residual does not follow AR or MA ...
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51 views

Checking that values are piecewise uniform

I have a set of values and I wish to check if they are piecewise uniform. I hope I'm using the correct terms, but I'll explain what I mean. Consider the following values - 100,105,100,103,98. We ...
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29 views

Adjusting time series for methodological change during the time period

The issue is that the national bureau of statistics changed permanently the variable calculation methodology during the overall period. Now I have two official time series for the same variable. One ...
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23 views

Problem using rsFit to calcualte Hurst Exponent

I am trying to calculate the hurst exponent using the Rescaled range Analysis. I'm using the rsFit function of the fArma package. To test it I create a bronwian motion "r" and the hurst should be .5 ...
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29 views

Financial Time series prediction/ SV Regression

I'm working with R software (Lib e1071) and I'm trying to get predictions using Support Vector Regression. The way I'm doing it is the following: I'm windowizing the raw closing prices using N=3 ...
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31 views

Using Real-Time Forecast Errors to Improve Forecast

I'm trying to forecast customer orders, and want to incorporate real-time forecast errors into my forecast. Say it's Monday, and I forecast that the customer will order 100 units on Wednesday. To ...
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28 views

How to measure the randomness of a time series?

I have at least two time series. How can I measure which one of them is more random than the others? I am also interested in monitoring the changes in the amount of randomness over time for an ...
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95 views

Sample ACF and PACF of a random walk

Suppose $X_n$are iid $N(0,1)$ random variables. Define $S_n := \sum_{i=1}^n X_n$. Then $S_n$ is a random walk. Since $Var(S_n) = n$ and $Cov(S_n, S_m) = \min(n,m)$, $S_n$ is not stationary in the ...
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66 views

ACVF and PACF of MA(q)?

Brockwell and Davis's book gives the autocovariance of a MA(q) process. I wonder if the magnitude of its autocovariance monotonically decreases before the lag $h$ increases over $q$? A note says ...
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37 views

Is there an “initial condition” for ARMA model?

ARMA model is a stochastic version of recursive relation. For deterministic recursive relations, we solve them and need initial conditions to fully get the solution. So I wonder what is an "initial ...
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79 views

Strict exogeneity and lagged variables

I am confused why strict exogeneity must be violated when we have lagged time series variables. My understanding of strict exogeneity is that a variable must be uncorrelated with error terms in all ...
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56 views

Improving Python Exponential smoothing

I am going to improve my code to the Exponential smoothing I submitted to Statsmodel which can be found here. The code handles 15 different variation Standard Exponential Smoothing models including ...
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17 views

Can p and q in ARMA(p,q) be estimated from its ACF and PACF?

From Wikipedia For AR(p), its p can be estimated from where its sample partial autocorrelation function (PACF) plot becomes zero. For MA(q), its q can be estimated from where its sample ...
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49 views

Can AR models be written as MA models?

I heard that $AR(1)$ can be written as $MA(\infty)$. Can $AR(p), p \in \mathbb N, p \ge 2$ be written as $MA(q)$ for some $q$? Thanks!
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83 views

Is there a white noise which is not ergodic?

Is there a white noise which is not ergodic? How is the ergodicty of a white noise tested? Thanks! Note: A white noise is defined as in Time Series: Theory and Methods By Peter J. Brockwell, ...
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1answer
38 views

How to tell stationarity from a sample path?

Given a sample path, we can roughly tell whether the mean changes over the time, and, when it doesn't, whether the deviation from mean changes over the time. (Correct me if I am wrong.) But that is ...
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24 views

Estimation of constant in MA(1) process using least square estimate

I would like to estimate the constant in MA(1) process using LSE, but am finding it very difficult.
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46 views

Time Period Predictive Modeling

I have been implementing some classification algorithms (Naive Bayes, SVM etc) recently on the iris data sets to get head start into the data science field. I enjoy working on machine learning ...
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18 views

Covariance between two sample means of correlated data

I have two sets of random data $X=\{x_1,...,x_N\}$ and $Y\{y_1,...,y_N\}$ both of length $N$. The sets are autocorrelated such that the correlation between $x_i$ and $x_j$ depends only on $|i-j|$. ...
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101 views

Confusion about the term “stochastic drift”

After reading lots of material about the subject, I believe that the term "stochastic drift" is defined in a two different ways. These two different definitions make the term unambiguous and I assume ...
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97 views

Testing “trends over time” of dummy variables

Let us say this is an output of a model I ran in Stata, where int_retis a continuous variable and time1-...